Question

show that the points A(6,4), B(9,7) and C(11,9) are collinear​

Answer 1

Answer:

$ab + bc = ca \\ \\ therefore \: \: \: \: \: points \: are \: collinear.$

Step-by-step explanation:

$a(6 \: \: \: \: \: \: \: \: \: 4) \: \: \: \: b(9 \: \: \: \: \: \: \: \: 7) \: \: \: \: c(11 \: \: \: \: \: \: \: \: \: 9) \\ \\ ab = \sqrt{ {(9 - 6)}^{2} + {( 7 - 4)}^{2} } \\ = \sqrt{9 + 9} \\ = 3 \sqrt{2} \: units \\ \\ \\ bc = \sqrt{ {(11 - 9)}^{2} + {(9 - 7)}^{2} } \\ = \sqrt{4 + 4} \\ = 2 \sqrt{2} \: units \\ \\ \\ \\ ca = \sqrt{ {(11 - 6)}^{2} + {(9 - 4)}^{2} } \\ = \sqrt{25 + 25} \\ = 5 \sqrt{2} \: units \\ \\ \\ \\ as \: \: \: \: \: \: \: \: \: \: \: \: ab + bc = ca \\ \\ therefore \: \: \: \: \: points \: are \: collinear.$